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Quantum adiabatic transfer is widely used in quantum computation and quantum simulation. However, the transfer speed is limited by the quantum adiabatic approximation condition, which hinders its application in quantum systems with a short decoherence time. Here we demonstrate quantum adiabatic state transfers that jump along geodesics in one-qubit and two-qubit superconducting transmons. This approach possesses the advantages of speed, robustness, and high fidelity compared with the usual adiabatic process. Our protocol provides feasible strategies for improving state manipulation and gate operation in superconducting quantum circuits.

Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting topological properties but have not been measured in non-Abelian systems. Here, we use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. By manipulating the Hamiltonian with periodic drivings, we simulate the Bernevig–Hughes–Zhang model and obtain the quantum geometric tensor from interference oscillation. In addition, we reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.

Quantum many-body systems in which time-reversal symmetry is broken give rise to a wealth of exotic phases, and thus constitute one of the frontiers of modern condensed matter physics. Quantum simulation allows us to better understand many-body systems with huge Hilbert space, where classical simulation is usually inefficient. With superconducting quantum circuit as a platform for quantum simulation, we realize synthetic Abelian gauge fields by using microwave drive and tunable coupling in loop configurations to break the time-reversal symmetry of the system. Based on high-precision manipulation and readout of circuit-QED architecture, we demonstrate the chiral ground spin current of a time-reversal symmetry broken system with nontrivial interactions. Our work is a significant attempt to simulate quantum many-body systems with time-reversal symmetry breaking in multi-qubit superconducting processors.

Stimulated Raman adiabatic passage (STIRAP) is a widely used protocol to realize high-fidelity and robust quantum control in various quantum systems. However, further application of this protocol in superconducting qubits is limited by population leakage caused by the only weak anharmonicity. Here, we introduce an optimally controlled shortcut-to-adiabatic (STA) technique to speed-up the STIRAP protocol in a superconducting qudit. By modifying the shapes of the STIRAP pulses, we experimentally realize a fast (32 ns) and high-fidelity (0.996 ± 0.005) quantum state transfer. In addition, we demonstrate that our protocol is robust against control parameter perturbations. Our stimulated Raman shortcut-to-adiabatic passage transition provides an efficient and practical approach for quantum information processing.

In a superconducting quantum processor with nearest neighbor coupling, the dispersive interaction between adjacent qubits can result in an effective next-nearest-neighbor coupling whose strength depends on the state of the intermediary qubit. Here, we theoretically explore the possibility of engineering this next-nearest-neighbor coupling to implement controlled two-qubit operations where the intermediary qubit controls the operation on the next-nearest neighbor pair of qubits. In particular, in a system comprising two types of superconducting qubits with anharmonicities of opposite-sign arranged in an -A-B-A- pattern, where the unwanted static ZZ coupling between adjacent qubits could be heavily suppressed, a switchable coupling between the next-nearest-neighbor qubits can be achieved via the intermediary qubit, the qubit state of which functions as an on/off switch for this coupling. Therefore, depending on the adopted activating scheme, various controlled two-qubit operations such as controlled-iSWAP gate can be realized, potentially enabling circuit depth reductions as to a standard decomposition approach for implementing generic quantum algorithms.

Scalable quantum information processing requires that modular gate operations can be executed in parallel. The presence of crosstalk decreases the individual addressability, causing erroneous results during simultaneous operations. For superconducting qubits which operate in the microwave regime, electromagnetic isolation is often limited due to design constraints, leading to signal crosstalk that can deteriorate the quality of simultaneous gate operations. Here, we propose and demonstrate a method based on the alternative-current Stark effect for calibrating the microwave signal crosstalk. The method is suitable for processors based on fixed-frequency qubits, which are known for high coherence and simple control. The optimal compensation parameters can be reliably identified from a well-defined interference pattern. We implement the method on an array of seven superconducting qubits and show its effectiveness in removing the majority of crosstalk errors.

Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on near-term intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.

The superconducting transmon qubit is currently a leading qubit modality for quantum computing, but gate performance in quantum processor with transmons is often insufficient to support running complex algorithms for practical applications. It is thus highly desirable to further improve gate performance. Due to the weak anharmonicity of transmon, a static ZZ interaction between coupled transmons commonly exists, undermining the gate performance, and in long term, it can become performance limiting. Here we theoretically explore a previously unexplored parameter region in an all-transmon system to address this issue. We show that an feasible parameter region, where the ZZ interaction is heavily suppressed while leaving XY interaction with an adequate strength to implement two-qubit gates, can be found for all-transmon systems. Thus, two-qubit gates, such as cross-resonance gate or iSWAP gate, can be realized without the detrimental effect from static ZZ interaction. To illustrate this, we demonstrate that an iSWAP gate with fast gate speed and dramatically lower conditional phase error can be achieved. Scaling up to large-scale transmon quantum processor, especially the cases with fixed coupling, addressing error, idling error, and crosstalk that arises from static ZZ interaction could also be strongly suppressed., 6 pages, 4 figures

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-$Z$ gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

Fast, robust two-qubit gate operation with low susceptibility to crosstalk are the key to scalable quantum-information processing. A parametrically driven gate is inherently insensitive to crosstalk, while superadiabatic control can speed up the gate without losing accuracy. We propose and experimentally implement superadiabatic two-qubit gates using parametric modulation on superconducting quantum circuits. Our results demonstrate the preservation of adiabaticity at a gate speed close to the quantum limit, in addition to robustness against control instability. We demonstrate a controlled-$Z$ gate with an error rate of $5.8\mathrm{%}$, mainly limited by qubit decoherence, promising future improvement and scalable implementation.

For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

As superconducting quantum circuits are scaling up rapidly towards the noisy intermediate-scale quantum (NISQ) era, the demand for electronic control equipment has increased significantly. To fully control a quantum chip of N qubits, the common method based on up-conversion technology costs at least 2 × N digital-to-analog converters (DACs) and N IQ mixers. The expenses and complicate mixer calibration have become a hinderance for intermediate-scale quantum control. Here we propose a universal control scheme for superconducting circuits, fully based on parametric modulation. To control N qubits on a chip, our scheme only requires N DACs and no IQ mixer, which significantly reduces the expenses. One key idea in the control scheme is to introduce a global pump signal for single-qubit gates. We theoretically explain how the universal gates are constructed using parametric modulation. The fidelity analysis shows that parametric single-qubit (two-qubit) gates in the proposed scheme can achieve low error rates of 10−4, with a gate time of about 60 ns (100 ns).

A semi-infinite waveguide acts as a mirror and helps protect the qubit in front of it from decoherence. Here, we investigate the interference effect in an open waveguide consisting of resonators with different decay rates. We find that a lossy resonator works as a mirror and changes the effective decay rate of the other. The spontaneous radiation of qubit is related to its environment, and we can control it by arranging the lossy resonator’s position or frequency. Our approach helps improving the qubit performance, as well as the quantum gate fidelities.

We demonstrate an active reset protocol in a superconducting quantum circuit. The thermal population on the excited state of a transmon qubit is reduced through driving the transitions between the qubit and an ancillary qubit. Furthermore, we investigate the efficiency of this approach at different temperatures. The result shows that population in the first excited state can be dropped from 7% to 2.55% in 27 ns at 30 mK. The efficiency improves as the temperature increases. Compared to other schemes, our proposal alleviates the requirements for measurement procedure and equipment. With the increase of qubit integration, the fast reset technique holds the promise of improving the fidelity of quantum control.

Possessing the noise-resilience feature, geometric phases have become important in robust quantum computation. Gates based on the Abelian and non-Abelian geometric phases have been experimentally demonstrated in different physical systems. However, previous proposals require cyclic evolution with a constant operation time even for small rotation angles, which set a limit to the gate operation time. Here, we experimentally realize noncyclic geometric gates, where the cyclic condition is removed and the operation time is proportional to the rotation angle. With the adiabatic process sped up by shortcut to adiabaticity, the fidelities of a noncyclic geometric gate characterized by randomized benchmarking are above 99.5%. Comparing with the dynamic scheme, we demonstrate the robustness of our gate against control instability in the experiment. Moreover, our results indicate that the noncyclic geometric gate with a smaller rotation angle corresponds to a shorter evolution time and higher fidelity. As small rotation angles are essential in the quantum algorithm, the superiority of noncyclic geometric gates makes them promising candidates in fast and robust quantum computation.

In superconducting quantum circuits, Josephson junctions are a key component to provide nonlinearity and enable superconducting qubits. Fabricating junctions with precise critical currents is crucial to defining qubit frequency. Here we suppress the critical current variation of Josephson junctions by varying the critical current density Jc and junction areas. The relative standard deviation of the critical current Ic is controlled to be below 0.8%. This uniform fabrication is promising for realizing scalable superconducting quantum computation.

Berry curvature is an imaginary component of the quantum geometric tensor (QGT) and is well studied in many branches of modern physics; however, the quantum metric as a real component of the QGT is less explored. Here, by using tunable superconducting circuits, we experimentally demonstrate two methods to directly measure the quantum metric tensor for characterizing the geometry and topology of underlying quantum states in parameter space. The first method is to probe the transition probability after a sudden quench, and the second one is to detect the excitation rate under weak periodic driving. Furthermore, based on quantum-metric and Berry-curvature measurements, we explore a topological phase transition in a simulated time-reversal-symmetric system, which is characterized by the Euler characteristic number instead of the Chern number. The work opens up a unique approach to explore the topology of quantum states with the QGT., Comment: 6 pages, 4 figures; newly cited two experimental references

We simulated highly tunable Weyl-semimetal bands using superconducting quantum circuits. Driving the superconducting quantum circuits with microwave fields, we mapped the momentum space of a lattice to the parameter space, realizing the Hamiltonian of a Weyl semimetal. By measuring the energy spectrum, we directly imaged the Weyl points, whose topological winding numbers were further determined from the Berry curvature measurement. In addition, we manipulated the band structure with an additional pump microwave field, producing a momentum-dependent Weyl-point energy together with an artificial magnetic field, which are indispensable for generating chiral magnetic topological currents in some special Weyl semimetals and may have significant impact on topological physics.

Shortcuts to adiabaticity have been proved an effective routine for precise quantum state manipulation. Here, we experimentally demonstrate invariant-based shortcuts to adiabaticity to speed up the population transfer in a superconducting circuit. Through inverse engineering of the Hamiltonian, we realize this protocol in a single-qubit and a two-qubit system. The Lewis–Risenfeld phase is characterized experimentally. Furthermore, we investigate the robustness of the scheme against amplitude and frequency errors.

Coherent quantum state transfer is a vital step in quantum information processing. Based on the stimulated Raman adiabatic passage (STIRAP), we realize robust quantum state transfer between two superconducting qubits, mediated by a tunable coupler. Utilizing parametric coupling techniques, we construct the STIRAP Hamiltonian by modulating the coupler frequency. A population transfer fidelity of 95.1 ( ± 2.0 ) % is achieved and is consistent with the numerical simulation result of 95.4%. By preparing the initial state in the maximal superposition state of one qubit, we research how the phase of the transferred state is related to the modulation pulses. We also find that the transfer process is robust against the fluctuation of modulation frequency. Numerical simulation confirms that our state transfer scheme is more robust than non-adiabatic protocols.

In quantum mechanics, although the no-cloning theorem forbids us to clone an arbitrary quantum state ideally, it is still possible to partially reproduce an unknown quantum state by using a phase cloning machine. Since the no-cloning theorem guarantees the safety of quantum key distribution (QKD), resulting in the famous Bennett–Brassard 1984 (BB84) protocol, phase cloning of BB84 states increases the probability to eavesdrop the transmitted information between correspondents, forcing us to recheck the security of the QKD protocol. In this work, we realize an optimal phase cloning machine for BB84 states in a superconducting quantum bit (qubit). The lowest three energy levels in this system are exploited as logical qubits to demonstrate this cloning procedure. Two microwaves are used to prepare and clone the states. In order to achieve the maximum fidelity, we use the state tomography to readout the experimental results. It is found that the state information is well preserved during this cloning process. The average fidelity between input and output states is 83.92%, making this a valid quantum cloning machine.

We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Three-fold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one., Comment: 6 pages, 4 figures; accepted version

We propose a realizable circuit QED architecture for engineering states of a superconducting resonator off-resonantly coupled to an ancillary superconducting qubit. The qubit-resonator dispersive interaction together with a microwave drive applied to the qubit gives rise to a Kerr resonator with two-photon driving that enables us to efficiently engineer the quantum state of the resonator such as generation of the Schrodinger cat states for resonator-based universal quantum computation. Moreover, the presented architecture is easily scalable for solving optimization problem mapped into the Ising spin glass model, and thus served as a platform for quantum annealing. Although various scalable architecture with superconducting qubits have been proposed for realizing quantum annealer, the existing annealers are currently limited to the coherent time of the qubits. Here, based on the protocol for realizing two-photon driven Kerr resonator in three-dimensional circuit QED (3D cQED), we propose a flexible and scalable hardware for implementing quantum annealer that combines the advantage of the long coherence times attainable in 3D cQED and the recently proposed resonator based Lechner-Hauke-Zoller (LHZ) scheme. In the proposed resonator based LHZ annealer, each spin is encoded in the subspace formed by two coherent state of 3D microwave superconducting resonator with opposite phase, and thus the fully-connected Ising model is mapped onto the network of the resonator with local tunable three-resonator interaction. This hardware architecture provides a promising physical platform for realizing quantum annealer with improved coherence., 13 pages, 9 figures

We propose an approach to simultaneously excite two atoms by using a cavity-assisted Raman process in combination with a cavity-photon-mediated interaction. The system consists of a two-level atom and a $\mathrm{\ensuremath{\Lambda}}$-type or $\mathsf{V}$-type three-level atom, which are coupled together with a cavity mode. Having derived the effective Hamiltonian, we find that under certain circumstances a single photon can simultaneously excite two atoms. In addition, multiple photons and even a classical field can also simultaneously excite two atoms. As an example, we show a scheme to realize our proposal in a circuit QED setup, which is artificial atoms coupled with a cavity. The dynamics and the quantum-statistical properties of the process are investigated with experimentally feasible parameters.

We present a model to describe a generic circuit QED system which consists of multiple artificial three-level atoms, namely qutrits, strongly coupled to a cavity mode. When the state transition of the atoms disobey the selection rules the process that does not conserve the number of excitations can happen determinatively. Therefore, we can realize coherent exchange interaction among three or more atoms mediated by the exchange of virtual photons. In addition, we generalize the one cavity mode mediated interactions to the multi-cavity situation, providing a method to entangle atoms located in different cavities. Using experimental feasible parameters, we investigate the dynamics of the model including three cyclic-transition three-level atoms, for which the two lowest-energy levels can be treated as qubits. Hence, we have found that two qubits can jointly exchange excitation with one qubit in a coherent and reversible way. In the whole process, the population in the third level of atoms is negligible and the cavity photon number is far smaller than 1. Our model provides a feasible scheme to couple multiple distant atoms together, which may find applications in quantum information processing., 10 pages, 6 figures

Symmetries of space-inversion (P), time-reversal (T), as well as the joint space–time inversion (PT) are fundamental and significantly important in physics. Here we have experimentally realized the joint PT invariant $${\Bbb Z}_2$$ Z 2 -type topological semimetal-bands, via an analogy between the momentum space and a controllable parameter space in superconducting quantum circuits. By measuring the whole energy spectrum of the system, we clearly imaged an exotic tunable gapless band structure typical of topological semimetals. Two topological quantum phase transitions, from a topological semimetal to two kinds of insulators, can be manipulated by continuously tuning the different parameters in the experimental setup, one of which captures the $${\Bbb Z}_2$$ Z 2 topology of the PT semimetal via merging a pair of nontrivial $${\Bbb Z}_2$$ Z 2 Dirac points. Remarkably, the topological robustness was demonstrated unambiguously, by adding a perturbation that breaks only the individual T and P symmetries but keeps the joint PT symmetry. In contrast, when another kind of PT-violating perturbation is introduced, a topologically trivial insulator gap is fully opened.

Using a multi-layered printed circuit board, we propose a 3D architecture suitable for packaging supercon- ducting chips, especially chips that contain two-dimensional qubit arrays. In our proposed architecture, the center strips of the buried coplanar waveguides protrude from the surface of a dielectric layer as contacts. Since the contacts extend beyond the surface of the dielectric layer, chips can simply be flip-chip packaged with on-chip receptacles clinging to the contacts. Using this scheme, we packaged a multi-qubit chip and per- formed single-qubit and two-qubit quantum gate operations. The results indicate that this 3D architecture provides a promising scheme for scalable quantum computing.

We investigate the XY control and manipulation of the superconducting qubit state using direct digital synthesis (DDS) for the microwave pulse signal generation. The decoherence time, gate fidelity, and other qubit properties are measured and carefully characterized, and compared with the results obtained by using the traditional mixing technique for the microwave pulse generation. In particular, the qubit performance in the state manipulation with respect to the sampling rate of DDS is studied. Our results demonstrate that the present technique provides a simple and effective method for the XY control and manipulation of the superconducting qubit state. Realistic applications of the technique for the possible future scalable superconducting quantum computation are discussed.

We propose and demonstrate experimentally the arbitrary state-transfer in a qubit by using a superadiabatic approach in a superconducting circuit. We encode the qubit in a time-dependent dark state generated by an applied microwave field, speeding up the adiabatic evolution by transitionless quantum driving algorithms. This approach is realized experimentally in a qutrit system, which consists of a qubit and an ancillary level. Furthermore, we analyze the robustness of the implementation and measure the fidelity of transfer operation by using randomized benchmarking technique.

We measured the switching from a superconducting state to a finite voltage state in a dc SQUID, which is equivalent to a single Josephson junction with tunable critical current Ic. The width and the mean of the switching current distribution depend on the effective temperature Teff and Ic. The phase-diffusion was observed by investigating the switching current distribution as a function of Teff. It is found that the crossover from the thermal activation to the phase-diffusion scaling with the ratio of Ic and Teff, clarifying the physical picture of the phase-diffusion. We developed an analytical multi-retrapping model which can address the experimental results very well.

Hopf-link semimetals exhibit exotic gapless band structures with fascinating topological properties, which have never been observed in nature. Here we demonstrate nodal lines with topological form of Hopf-link chains in artificial semimetal-bands. Driving superconducting quantum circuits with elaborately designed microwave fields, we mapped the momentum space of a lattice to a parameter space of the Hamiltonian for a Hopf-link semimetal. By measuring the energy spectrum, we directly imaged nodal lines in cubic lattices. By tuning the driving fields, we adjusted various parameters of Hamiltonian. Important topological features, such as link-unlink topological transitions and the robustness of the Hopf-link chain structure were investigated. Moreover, we extracted the linking number by detecting the Berry phase associated with different loops encircling nodal lines. This topological invariant clearly reveals the nontrivial topology of the Hopf-link semimetal. Our results provide knowledge for developing new materials and quantum devices., Comment: 6 pages, 4 figures. arXiv admin note: text overlap with arXiv:1702.01512

We propose and experimentally demonstrate a scheme to simulate the interaction between a two-level system and a classical light field. Under the transversal driving of two microwave tones, the effective Hamiltonian in an appropriate rotating frame is identical to that of the general semi-classical Rabi model. We experimentally realize this Hamiltonian with a superconducting transmon qubit. By tuning the strength, phase, and frequency of the two microwave driving fields, we simulate the quantum dynamics from the weak to extremely strong driving regime. Under these conditions, we observe that, as a function of increased Rabi drive strength, the qubit evolution gradually deviates from the normal sinusoidal Rabi oscillation, in accordance with the predictions of the general semi-classical Rabi model far beyond the weak driving limit. Our scheme provides an effective approach to investigate the extremely strong interaction between a two-level system and a classical light field. Such strong interactions are usually inaccessible in experiments.

The Kibble-Zurek mechanism (KZM) predicts the density of topological defects produced in the dynamical processes of phase transitions in systems ranging from cosmology to condensed matter and quantum materials. The similarity between KZM and the Landau-Zener transition (LZT), which is a standard tool to describe the dynamics of some non-equilibrium physics in contemporary physics, is being extensively exploited. Here we demonstrate the equivalence between KZM in the Ising model and LZT in a superconducting qubit system. We develop a time-resolved approach to study quantum dynamics of LZT with nano-second resolution. By using this technique, we simulate the key features of KZM in the Ising model with LZT, e.g., the boundary between the adiabatic and impulse regions, the freeze-out phenomenon in the impulse region, especially, the scaling law of the excited state population as the square root of the quenching rate. Our results supply the experimental evidence of the close connection between KZM and LZT, two textbook paradigms to study the dynamics of the non-equilibrium phenomena., Title changed, authors added, and some experimental data updated

We propose a scheme to perform two-qubit state tomography by independently measuring the ensemble average of quantum states of two coupled superconducting transmon qubits. Each qubit is capacitively coupled to its own readout cavity and can be measured separately. In order to obtain the density matrix of a two-qubit state, we apply four two-qubit unitary operations to the initial state and measure the corresponding qubit states, from which the elements of the two-qubit density matrix can be extracted. By using this scheme, we measure the entangled two qubits with high fidelity.

Geometric quantum manipulation and Landau-Zener interferometry have been separately explored in many quantum systems. In this Letter, we combine these two approaches to study the dynamics of a superconducting phase qubit. We experimentally demonstrate Landau-Zener interferometry based on the pure geometric phases in this solid-state qubit. We observe the interference caused by a pure geometric phase accumulated in the evolution between two consecutive Landau-Zener transitions, while the dynamical phase is canceled out by a spin-echo pulse. The full controllability of the qubit state as a function of the intrinsically robust geometric phase provides a promising approach for quantum state manipulation., Comment: 5 pages + 3 pages supplemental Material

Superconducting quantum circuits are promising candidates for realizing quantum computation due to their intrinsic scalability. Here, we report the implementation of the refined Deutsch–Jozsa algorithm in a 3D superconducting transmon qutrit system. Such 3D superconducting systems usually preserve a relatively long coherence time. A qutrit can take advantage of the third level of a superconducting artificial atom and extends the Hilbert space. Compared with the two-qubit system used for realizing Deutsch–Jozsa algorithm, the employment of qutrit simplifies the hardware design. This simplification and the intrinsic long coherence time jointly lead to a higher fidelity than in previous transmon implementation [DiCarlo et al., Nature 460 (7252), 240–244 (2009)].

We fabricate high-quality Al/AlO x /Al junctions using improved bridge and bridge-free techniques at 30-keV e-beam voltage, in which the length of undercut and the size of junction can be well controlled by the pre-exposure technique. The dose window is 5 times as large as that used in the usual Dolan bridge technique, making this technique much more robust. Similar results, comparable with those achieved using a 100-keV e-beam writer, are obtained, which indicate that the 30-keV e-beam writer could be an economic choice for the superconducting qubit fabrication.